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Summary Notes

These are summary notes so that you can really listen in
class and not spend the entire time copying notes. These
notes will not substitute for reading the chapters in the
text, nor can they replace the text as there are many subtleties
we will discuss in class that are also presented in the text.
Use these as a supplement.

1.1 Arguments, Premises and
Conclusions

Concepts:

These are terms you should be able to define
and recognize after covering Section 1.1.

definition of logic

definition of an argument
You will be responsible for memorizing this definition
(word for word) on the first quiz and midterm. It is
the only instance when I will ask you to memorize material
in this fashion.

statement

truth values: statements are either
true or false

premise & conclusions indicators

Know the difference between "For this reason" and "for
the reason that."

Not all arguments have premise
and conclusion indicators.When you are faced with
such an argument attempt to find the "topic sentence" or
main point of the argument. Good bets for its location
are the first or last sentence of the argument.

1.2 Recognizing Arguments

Concepts:

These are terms you should be able to define
and recognize after covering Section 1.1.

factual claim

inferential claim : explicit & implicit

two uses of the word "since" temporal versus
logical sense

the role of interpretation in evaluating information/arguments

Non-arguments lack inferential claims

Be careful to note that reports, explanations, expository
passages and illustrations as well as arguments may look
quite similar and the author is often inconsistent when
he applies these labels in the exercises that follow.

Breakdown:

Passages lacking an inferential claim:

Warnings: often end in an exclamation point.

Pieces of Advice

Statements of Opinion: these must always be supported
by evidence to be considered arguments in the strict logical
sense.

Loosely Associated Statements: these are statements
in which the premise will not bear any common-sense or
logical relation to the conclusion.

Report: absent here is the claim that the statements
support or imply anything; report passages should read
like a chronicle of events without the interjection of
opinion.

Expository passage: just as it sounds, this is
merely an explanation.

NOTE: some
passages can be interpreted both as expository passages
and as arguments.

Illustration: statement and examples that further
clarify the category being discussed. For our class, think
of an illustration as a set of instructions, a how-to procedure.

Explanations:

Two Parts:

Explanans: "statement or group of statements
that purports to do the explaining" reasons.

Explanandum: "statement that describes the event
of phenomenon to be explained"

Note: the
method for distinguishing arguments from explanations;
there must be an element of persuasion present to
classify a passage in the argument category. If a
passage presents generally known facts, then it is
an explanation.

Conditional Statements:

These are "if then" statements.

Review the definition of antecedent & consequent.

One conditional statement
does not an argument make.

Note the rules for recognizing conditional statements
as arguments.

Context is everything and the intended audience plays
a large role in determining what the context actually is.

There is a wealth of ambiguity here. Note the paragraph
on mid-21 about explanations that resemble arguments.

Language Patterns for syllogisms & examples:

A set of three statements placing objects/persons
into categories/groups.

The statements always begin with the words:
All, No or Some.

The pattern:

All cats are mammals.

All mammals are animals.

\ All
cats are animals.

Some fish are not trees.

No trees are plants.

\ Some
fish are not plants.

Hypothetical Syllogisms:

A conditional statement (If [antecedent]______,
then _[consequent]_____.) paired with two other
statements that repeat the antecedent and consequent.

The pattern:

If I receive a paycheck this week,
then I should be able to pay the bills.

I received a paycheck this week.

\ I
should be able to pay the bills.

If the snow total runs over 35" this
season, then we will need more money to salt the
roads.

We will not need more money
to salt the roads.

\ The
snow total is not over 35".

Disjunctive Syllogisms:

An Either _______ or ________. statement paired with
two other statements in which one alternative is eliminated
and we are left with the remaining alternative.

The pattern:

Either we pay the rent or we will
be evicted.

We did not pay the rent.

\ We
will be evicted.

.

Either taxes will be raised or
we will run up large deficits.

Taxes will not be raised.

\ We
will run up large deficits.

Factors that help us decide between deductive and inductive
arguments:

The presence of indicator words.

The "actual strength of the
inferential ink between premises and conclusions."

Instances in which the conclusion does not follow from
the premises either necessarily or probably.

The easiest way to learn to distinguish deductive from
inductive arguments is to learn to recognize the deductive
argument forms on sight. If your argument does not
follow the form [i.e., language pattern] of a deductive
argument, then it is necessarily inductive by the process
of elimination.

Some cautions/notes from reading:

Geometric arguments are always deductive

Scientific arguments can be either
inductive or deductive.

The common definition for distinguishing
between deductive and inductive arguments (general/particular)
does not hold.

1.4 Validity, Truth, Soundness & Cogency

Valid Deductive Arguments

Validity is determined by the relationship between premises
and conclusion.(i.e., Ask yourself: do the premises support
the conclusion?)

View chart in Section 1.4. Note that all invalid arguments
are unsound.

Sound argument = true premises, true conclusion Both
conditions must be met for an argument to be sound. There
is only one kind of sound argument.

Inductive Arguments

Strong Inductive Argument = "improbable
that premises are true and conclusion is false"

Strong arguments have a probability of 51%
or greater. The conclusion, however, is not
guaranteed, it is only likely.

"A cogent argument is strong and has
all true premises; if either condition is missing,
the argument is uncogent."(50) In a cogent
argument the premises must not ignore relevant
information that would make them untrue.

Weak Inductive Argument = "conclusion
does not follow probably from the premises"

Read section on probabilistic support;
support is at issue here, not the truth or
falsity of the premises.

Notice that there is only one type of
sound, cogent argument: true premises, true
conclusion.

1.5 Argument Forms: Proving Invalidity

Numbers in parenthesis refer to page numbers in the text.

This week we are looking at the validity/invalidity of deductive
arguments. "The validity of an argument has nothing to
do with its specific subject matter. ...Its validity rests
purely upon the arrangement of the letters within the statements
and it has nothing to do with what the letters might stand
for."

The process of "uniformly substituting terms or statements
in place of the letters in an argument form is called a substitution
instance of that form."

Valid Form: Categorical
Syllogism

Invalid Form:
Categorical Syllogism

All A are B.

All B are C.

All A are C.

All A are B.

All C are B.

All A are C.

Counterexample Method:

WHY IS IT USEFUL?:
We use the counterexample method to prove invalidity; it
cannot be used to prove validity.

APPLICATION: This
technique is commonly used in the legal field to
show that the opponents argument does not hold together.
Another situation in which we routinely hear counterexamples
is during political debates when one opponent
attempts to discredit the other's arguments by providing
parallel examples that expose the absurdity of the
underlying logical structure. View any op-ed page in
a major newspaper and you are sure to find at least
one counterexample.

HOW DOES IT WORK? This
method proves an argument invalid by generating an example
of a given argument form with true premises and a false
conclusion.

Please note that the technique of using
a counterexample to prove arguments invalid only
works for deductive arguments.

STEP-BY-STEP METHOD FOR PROVING AN ARGUMENT INVALID
BY THE METHOD OF COUNTEREXAMPLE:

Locate the conclusion of the argument.

Symbolize the given argument using statement letters
in place of phrases. This reveals the argument's form.

Consistently substitute the generic terms: cats,
dogs, mammals, fish and animals to generate an argument with
true premises and a false conclusion.

It is helpful to begin your term substitutions with
the conclusion by choosing two terms that make it false.

Next, work through the premises selecting a third term
that makes the premises true.

If you are presented with a hypothetical syllogism, try
using the suggested substitutions in Section 1.5: e.g., Abraham
Lincoln, suicide and dead. The goal is to use terms that
have a necessary connection (e.g., rain-wet, snow-cold, suicide-dead).

If the conclusion is a conditional statement, join a true
antecedent with a false consequent.

Things to remember when working on substitution:

Be sure to separate form words from content words. Form
words for categorical and hypothetical syllogisms are: "all", "no", "some", "are", "not", "if",
and "then." In addition, other types of deductive
arguments include the form words: "either", "or", "both",
and "and."

Remember the word "some" means "at least
one" in logic.

This technique is difficult at first, but like other challenging
endeavors, will get easier with practice. Thus, you
should try to do as many problems as you can to gain skill
and confidence.

If you are struggling with a particular problem
and cannot generate a counterexample, move on to other
problems and return to the difficult one later.